In the triangle ABC AB = BC, height BH = 12, area = 60. find the length of the side AB.

1. Calculate the length of the AC side of the given triangle ABC. To do this, we use the formula for calculating the area (S) of a triangle:

S = AC x BH / 2.

AC = 2S / BH = 2 x 60/12 = 120: 12 = 10 units.

2. By the condition of the problem AB = BC. Hence the given triangle is isosceles.

3. The height BH also serves as a median and divides the side to which it is drawn into equal segments

AH = CH = AC / 2 = 10: 2 = 5 units.

4. We calculate the length of the side AB:

AB = √AN² + BH² = √5² + 12² = √25 + 144 = √169 = 13 units.

Answer: AB = 13 units.